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Mat. Zametki, 2009, Volume 86, Issue 3, Pages 469–473 (Mi mz8506)  

This article is cited in 7 scientific papers (total in 7 papers)

Brief Communications

Semiclassical Approximation for a Nonself-Adjoint Sturm–Liouville Problem with a Parabolic Potential

V. I. Pokotilo, A. A. Shkalikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Keywords: Sturm–Liouville problem, Orr–Sommerfeld operator, spectral graph, velocity profile, small parameter, analytic function, Stokes lines, entire function

DOI: https://doi.org/10.4213/mzm8506

Full text: PDF file (281 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2009, 86:3, 442–446

Bibliographic databases:

Received: 24.03.2009

Citation: V. I. Pokotilo, A. A. Shkalikov, “Semiclassical Approximation for a Nonself-Adjoint Sturm–Liouville Problem with a Parabolic Potential”, Mat. Zametki, 86:3 (2009), 469–473; Math. Notes, 86:3 (2009), 442–446

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ishkin Kh.K., “Conditions for localization of the limit spectrum of a model operator associated with the Orr-Sommerfeld equation”, Dokl. Math., 86:1 (2012), 549–552  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. Esina A.I. Shafarevich A.I., “Analogs of Bohr-Sommerfeld-Maslov Quantization Conditions on Riemann Surfaces and Spectral Series of Nonself-Adjoint Operators”, Russ. J. Math. Phys., 20:2 (2013), 172–181  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. I. Esina, A. I. Shafarevich, “Asymptotics of the Spectrum and Eigenfunctions of the Magnetic Induction Operator on a Compact Two-Dimensional Surface of Revolution”, Math. Notes, 95:3 (2014), 374–387  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Tumanov S.N. Shkalikov A.A., “the Limit Spectral Graph in Semiclassical Approximation For the Sturm-Liouville Problem With Complex Polynomial Potential”, Dokl. Math., 92:3 (2015), 773–777  crossref  mathscinet  zmath  isi  scopus
    5. D. V. Nekhaev, A. I. Shafarevich, “A quasiclassical limit of the spectrum of a Schrödinger operator with complex periodic potential”, Sb. Math., 208:10 (2017), 1535–1556  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Shafarevich A., “Quantization Conditions on Riemannian Surfaces and Spectral Series of Non-Selfadjoint Operators”, Formal and Analytic Solutions of Diff. Equations, Springer Proceedings in Mathematics & Statistics, 256, ed. Filipuk G. Lastra A. Michalik S., Springer, 2018, 177–187  crossref  mathscinet  isi
    7. Kh. K. Ishkin, R. I. Marvanov, “On localization conditions for spectrum of model operator for Orr–Sommerfeld equation”, Ufa Math. J., 12:4 (2020), 64–77  mathnet  crossref  isi
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